Lens Mathmatics for dummies

[Louis_Dobson]

it can't use the whole "A" (aperture at the front element). It isn't so much the 200 can't be f3.5, as the 50 can't be f1.8 (or whatever). But that's still the principle of why the f numner rises with the focal length, and I still don't understand why constant aperture zooms aren't wasting light...

In passing, I assume the fact that at the short lengths zooms can't use the whole front element is why most zooms soften at the long end.

But someone who understands optics properly needs to explain all this stuff.
--
http://www.flickr.com/photos/acam

 

[KSPhotog]

First off not a math whiz kinda dude...far from it. So I can't get into a techie discussion with some here but I can only go what I see and what I shoot. In the past I've owned Canon, Nikon and Pentax and even a Mamiya 645 (film and with a Kodak DCS 14MP back).

But by just looking at results say with the 35-100 f2 and using it...

Yes the what I would just "fall off" or depth of field seems closer f4 than say a Canon 70-200 2.8 shot at 2.8. I would still say it would just depend on what you're shooting (what's in the background and what effect you are looking for) I can shoot wide open at 2 and get the same look as wide open on a 2.8 C or N in certain situations (light, subject, background, etc).The bokeh is less pronounced...you still get that groovy 3D effect but it is different. I will tell you this: Oly lenses at F2 are just crazy sharp.

That 35-100 is a 70-200. Try it side by side with a full frame like a 5D or a D3 Nikon and you will see the distance is the same.

That all being said....F2 is F2. We all know the sensor is smaller so Oly went the distance for us and made F2 lenses to gather the maximum amount of light on the small sensor. Shooting my 14-35 f2 wide open gives me the same "fall off" as shooting somebody else at f2.8. Sometimes getting that nice round globe effect with the bokeh can be hard...depending on what is in the background but it can be done. I just bought the PanLeica 25mm 1.4 I suspect it will be easier with that lens.

Anywho....sorry not a math whiz but that's what I see.

Happy Shooting,

Chuck

--

'A hundredth of a second here, a hundredth of a second there - even if you put them

end to end, they still only add up to one, two, perhaps three seconds, snatched from
eternity.' Robert Doisneau

 

[Jonathan Demarais]

If "equivalence" as espoused by your mate, Joseph James (joe mama)
were correct, no light meter would work, and no exposure could ever
be calculated.

You are not really getting what equivalence means, do you? It means
that a 50mm f/2 on 4/3 gives similar images to a 100mm f/4 on full
frame assuming that you bump the ISO two stops. Exposure works fine
that way.

Get an ultra-basic book on exposure, Sergey - AND read it ...

And please read the arguments of other posters.

Ray, f2 is always f2. "Equivalence" is just b/s spruiked by the c/n
trolls to try to suggest that somehow an Olympus f2 lens is slow,
just like a c/n f4 lens is ...

It's a bit cheap to play the troll card, don't you think? I'm an
Olympus user myself, and know a fair bit about physics and
mathematics and it's all pretty obvious if you juggle the equations -
and keep an open mind.

An f2/35~100 lens is a very fast, very high quality lens.

That is true, but it may not be much more useful than a 70-200 f/4 on
full frame. [It could still be a better lens than any particular
70-200 f/4, of course]

Simon

From a mathematical standpoint, a lens is a lens and no sensor or film alters that fact. A 100mm lens at f2 does not "function" differently on a 4/3rds sensor than it does on a 35mm sensor, if you choose to compensate for an aspect of sensor characteristics (like higher noise), that has nothing to do with the lens's function and never will. Even the "2 stop" noise advantage is too crude to use as any kind of "standard" by which to gauge a sensor's behaviour with a lens. Is a Nikon D3 the same as Canon's 5D when it comes to noise? No! But they are both (more or less) 35mm sensors.
--



'I cried because I had no E-3. Then I met a man with no E-510'

Olympus E-410, E-330, Pentax K20D. 40 lenses of various types

 

[Juergen Hahn]

Louis has accurately answered your questions in his first two posts.

Unfortunately, the discussion gets sidetracked after that.

BTW, I cannot imagine that I ever need less DOF than I get with f2 on a 4/3 system. Other people may disagree, however, this is based upon my needs and from my observations.

 

[simpy]

But in speed terms you'll be able to stop down faster mouvements as
it is a F2 lens...

Point is that you can do the same with an F4 lens if you bump the ISO two stops. And you can push the ISO two stops further on a larger camera, not because of various idiosyncrasies of sensor technology, but because being larger, it collects four times as much light for a given f-stop.

Simon

 

[BillZM]

We repeat this topic over and over and over again in this forum, with two camps disagreeing or agreeing to disagree.

Some say f ratio is f ratio (true for calculating exposure); often these are advocates of 4/3 or APS "crop" cameras.

Some say full-frame 35mm sensor cameras can be stopped down to generate same DOF, bumping ISO (no problem as FF35 sensor has same noise performance at higher ISO as smaller sensor at larger ISO) to maintain same shutter speed, to produce the same image (this argument assumes same number of pixels between cameras); often these are advocates of full frame 35mm cameras.

Inevitably this leads to some concession that the full-frame advocates are largely right, but producing quality super wide angle lenses to support FF35 cameras is difficult (at reasonable size and expense). And sometimes a discussion about dust busters.

Unfortunately these threads usually max out at 150 posts with feelings hurt, egos bruised, etc.

I'd suggest you do searches for earlier threads. You'll probably find them by searching for: DOF 5D

 

[simpy]

From a mathematical standpoint, a lens is a lens and no sensor or
film alters that fact.

Certainly a valid viewpoint. There is nothing wrong with using f-numbers and ISO values as they come. However, looking at equivalent lenses for different sensors is not wrong either, it's just a different way of doing things. Note that I only reacted to John King's anti-equivalence rant.

A 100mm lens at f2 does not "function"
differently on a 4/3rds sensor than it does on a 35mm sensor, if you
choose to compensate for an aspect of sensor characteristics (like
higher noise), that has nothing to do with the lens's function and
never will.

Tell me, do you ever talk about 35mm-equivalent focal lengths? Doing so also takes the sensor size into account. Talking about f-number equivalences is no different. You don't need to do it, but it can be very convenient and illuminating.

Even the "2 stop" noise advantage is too crude to use as
any kind of "standard" by which to gauge a sensor's behaviour with a
lens. Is a Nikon D3 the same as Canon's 5D when it comes to noise?
No! But they are both (more or less) 35mm sensors.

You talk about 'the two stop advantage' as if it is some experimentally determined number. However, the number comes from the fact that the amount of light that is available to the sensor scales with the sensor area. A full frame sensor collects four times as much light for any given f-stop and exposure time. If it and a 4/3 sensor are equally efficient, the larger sensor has a two stop advantage - or, in other words, you can multiply the f-number by two to get the same amount of light on the sensor.

In other words, even though any particular 35mm sensor may not have a two stop advantage over a 4/3 sensor, you can expect that to be the case on average .

So, again, I'm not saying 'F2 is not F2'. It is perfectly fine to use F-stops and ISO values. However, please consider that another, equivalent (pun intended) system is valid as well - and may be more convenient when comparing systems.

Simon

 

[Ehrik]

I'm no lens designer, but I think I can answer this.

1:fn = A/fl.

So as you zoom A stays the same but fl changes, so the lens becomes
"slower".

Worth noting here is that A isn't the physical hole inside the lens,
but the entry pupil, that is, how big the hole LOOKS when looking into
the lens through the front element (easier when the lens is not mounted).

As to why some of the expensive ones don't, I wish I knew. I have a
horrible suspicion that it is related to the daft snobbery of
constant aperture zooms (which of course they are not anyway, they
are constant f number zooms), and the poor things are throttled at
the short end to please poseurs. I hope I'm wrong, but I'm waiting
for someone to explain.

Even though the physical size of the hole is the same, how big it looks
when zooming is determined by the lens design. If the lens design is
made to enlarge the entry pupil (the look of this hole) at the same rate
as the focal length goes up, the f-stop will stay constant.

So you don't need to be afraid of the lens being throttled to please
poseurs (you have a great way with words, BTW ). However, I
expect the extra constraint makes the lens harder to design so there
is no free lunch as usual.

Just my two oere
Erik from Sweden

 

[Juergen Hahn]

Here is a really good tutorial for what you are asking for:

http://www.cambridgeincolour.com/tutorials/digital-camera-sensor-size.htm

It covers all the comparisons between DOF, lens seize and weight, sensor cost (for different sizes, and light gathering capabilities.

 

[Juergen Hahn]

You talk about 'the two stop advantage' as if it is some
experimentally determined number. However, the number comes from the
fact that the amount of light that is available to the sensor scales
with the sensor area. A full frame sensor collects four times as much
light for any given f-stop and exposure time.

Do you have a source to back this up? I highly doubt that this is correct. Just because the sensor is 4 times as big does not mean that it receives 4 times the amount of light, as the amount of light that reaches the sensor is restricted prior to reaching the sensor.

Also, how do you explain this statement:

"Another important result is that if depth of field is the limiting factor, the required exposure time increases with sensor size for the same sensitivity." followed by

"On the other hand, exposure times may not necessarily increase as much as one might initially assume because larger sensors generally have lower noise (and can thus afford to use a higher sensitivity ISO setting while maintaining similar perceived noise)."
from
http://www.cambridgeincolour.com/tutorials/digital-camera-sensor-size.htm

What this means is that for light gathering capability f2 is f2, regardless of what system you look at. So you are going to have to compare f2 at 100 ISO with f4 at 400 ISO when it comes to light gathering capability.

What it comes down to is that
f2, 35-100mm, ISO 100 on 4/3 is equivalent to
f4, 70-200mm, ISO 400 on FF.

Obviously, ISO 400 on FF is better than ISO 400 on 4/3 (for similar number of MP on the sensor) as the detectors can be a lot bigger.

I am not trying to point out advantages/limitations of different systems here, however, let's just make a fair comparison.

 

[S N G]

From a mathematical standpoint, a lens is a lens and no sensor or
film alters that fact. A 100mm lens at f2 does not "function"
differently on a 4/3rds sensor than it does on a 35mm sensor, if you
choose to compensate for an aspect of sensor characteristics (like
higher noise), that has nothing to do with the lens's function and
never will.

I am afraid Olympus will disagree with you here, otherwise they would not be putting stickers on their lenses telling what 50-200 on 4/3rd is equivalent to on 35mm format. A lens is a lens - that is an interesting argument.

• sergey

 

[S N G]

When we speak speed we also mean ISO (for the same DoF). For the same
results you need to compare f/2 -> f/4 with ISO100-> ISO400,
ISO200-> ISO800, ISO400-> ISO1600, ... and so on.

• sergey

Excuse me. I think it is not always necessary for us to consider ISO
speed an advantage of FF because it is only meaningful when light
becomes a limiting factor.

When there is plenty of light, or when we are using artificial
illumination, there is usually no need to use high ISO. Basically,
the speed of f/2 on 4/3 system is exactly the same as f/2 on 35mmFF
system.

Ray, I do not disagree with you. But ask yourself, why do we need f/2?
1) Shallow DoF - FF can do at f/4 what 4/3rds does at f/2
2) Speed and less noise - FF can do at two stops higher than 4/3rd ISO
whenever necessary and deliver the same results

And with all other dSLR formats in between.

Of course, the dof of 4/3 is always around 2 stops deeper, but to me
it is sometimes an advantage sometimes a disadvantage.

It can only be an advantage when other system can not do the same. And as we know it, whatever 4/3rd can do the larger formats do with ease. "Advantage" therefore is not a correct word for this relationship, quite opposite applies better.

I think the only advantage of FF is mainly on hand-held portrait and
action photography at low light.

No, this the only advantage for you . I could bring you few more points for both sides, but then it would be for me , and pretty much outside the scope of this discussion.

..

• sergey

 

[BillZM]

Do you have a source to back this up? I highly doubt that this is
correct. Just because the sensor is 4 times as big does not mean that
it receives 4 times the amount of light, as the amount of light that
reaches the sensor is restricted prior to reaching the sensor.

Why do you assume this??? The claim that lenses at same f ratio project 4 times as much light per pixel (assuming same pixel count and same shutter speed) for a sensor of 4x the area is simply geometry. If the sensor has 4x the area, and pixel count is the same, each pixel also has 4x the area (assuming the vast majority of the sensor surfaces are comprised of microlenses feeding pixels and not circuitry). f ratio determines the light intensity (light per area), not total light. You ask for sources to prove this??? Perhaps the independent articles referenced in the thread?

But your statement that the amount of light that reaches the sensor is restricted prior to reaching the sensor (and your inference that this would favor the smaller sensor camera) WOULD require confirmation of some type. It is true, I think, that size/weight/cost restrictions might cause a lens manufacturer to market a lower cost/weight lens for FF35 which has more light falloff in the corners than is typical for Olympus ZD lenses. But overall illumination would still be as expected at the given f ratio. To overcome the 2 stops of geometrical advantage, you'd need severe restriction of light in the larger camera as though you had a 4x ND filter in place!

I'm not looking to prolong this debate (which we seem to have once a month in perpetuity). 4/3 is my system of choice. But I found your one statement curious.

 

[S N G]

....

Also, how do you explain this statement:
"Another important result is that if depth of field is the limiting
factor, the required exposure time increases with sensor size for the
same sensitivity."

If you shoot from the same spot and with the same focal length lens and with the same settings you will not get the same projected image on FF camera as you get on 4/3rd camera. For the same frame you need to either 1) come closer to the subject (DoF becomes shallower), or 2) take two times longer lens (DoF becomes shallower again). In both cases to compensate for loss of DoF you will need to stop the lens down, thus reduce the exposure. The loss of exposure is easily correctable by raising ISO, as explained in the next paragraph you quoted.

followed by
"On the other hand, exposure times may not necessarily increase as
much as one might initially assume because larger sensors generally
have lower noise (and can thus afford to use a higher sensitivity ISO
setting while maintaining similar perceived noise)."
from
http://www.cambridgeincolour.com/tutorials/digital-camera-sensor-size.htm

• sergey

 

[BigBen08]

Here's a new book all about lenses:

David Busch's Quick Snap Guide to Using Digital SLR Lenses.

I got the book about 2 wks ago. It answers many of the questions posted here.

Tells you about everything you need to know about selecting and using various types of dslr lenses. Lots of theory as well as practical info. A great book, IMHO.

 

[Juergen Hahn]

Why do you assume this??? The claim that lenses at same f ratio

project 4 times as much light per pixel (assuming same pixel count
and same shutter speed) for a sensor of 4x the area is simply
geometry.

Unfortunately, you are wrong on this. It is simple geometry that this light has passed through an opening of the same size and no matter what size the screen (in this case the sensor) behind it, the same amount of light will get through.

This is really rather simple geometry, however, people still do not get it right and then start debates like this.

But your statement that the amount of light that reaches the sensor
is restricted prior to reaching the sensor (and your inference that
this would favor the smaller sensor camera) WOULD require
confirmation of some type.

Have you looked at the back of your lenses to see where the light leaves the lens? Do you think that your lens physically changes when I mount it on a FF body as compared to an APS-C size body? The lens does not change and neither does the amount of light that goes into or out of your lens, regardless of what sensor size you have.

Also, what do you think happens when you change apertures? The opening that the light coming from the lens passes through changes in diameter. This is what restricts the amount of light passing, through, and not the size of the sensor.

 

[Juergen Hahn]

Sergey,

What you posted is not what I stated as you can see from the text that you even quoted. Please stay on topic and do not try to steer this away.

If you use the same DOF then you need to use higher ISO to get the same sensitivity. That is what I stated. No none said that you shoot an object from the same distance. That is a very different matter but is not what was discussed here.

Juergen

 

[Kirasir]

Ray, I do not disagree with you. But ask yourself, why do we need f/2?
1) Shallow DoF - FF can do at f/4 what 4/3rds does at f/2

You have forgotten to add "if shooting from the same place using the lens with the same AOV". Because otherwise 4/3 sensor CAN provide the same or more shallow DOF at f/4, as FF. The demand "same distance, same AOV" seem to be reasonable... but it only seems to be - it has nothing common with the real life and real photography.

2) Speed and less noise - FF can do at two stops higher than 4/3rd ISO
whenever necessary and deliver the same results

This statement also seems to be true, but only seems to be. A lot of times I have asked my colleagues with 1Ds Mk II, working on the same event, what sensitivity are they using just now. And each time it turned out, that just the same, as I used. And usually no higher than 400...

You are speaking about "two stops in ISO between 4/3 and FF" as if it's some law of nature. But difference of E-3 and 5D is less than one stop, and it can be seen only at iso higher than 1600. Don't believe me?
This comparison was already posted here:
"



"

There is great difference in noise performance between 5D and D3, and even greater between different cameras with the same APS sensor size.

It can only be an advantage when other system can not do the same.
And as we know it, whatever 4/3rd can do the larger formats do with
ease. "Advantage" therefore is not a correct word for this
relationship, quite opposite applies better.

Probably You are right. But it also means that You are wrong, and larger sensors do not have any DOF advantages too. They can obtain the same result changing two parameters, f-number and sensitivity, smaller sensors can obtain the goal also by changing two parameters, focal length and distance.

All theese discussion is just rubbish, but You time by time take out from the grandpa's barn all that covered by moss ideas.... In Russian photocommunity it's called photo-automanipulation. Better go and shoot some good photos, and show them. This will be much more usefull.

--
From Russia with Love -
Andrey Sudbin, Offroad journalist

 

[BillZM]

You are missing the fundamental argument here. To form the same image, the larger camera has a physically larger lens, scaled up from the 4/3 by 2x. The equivalent image is formed (as you cite in your own example in a previous post I believe) as such:

4/3 50 f2 lens gives the same image as FF35mm 100 f4 lens. Same FOV, same DOF, same total light captured, projected onto the same number of pixels (assuming the two sensors had the same pixel count).

The aperature in mm is the same for 50mm f2 as for 100mm f4. That's the equivalence people are discussing (you included I think in prior posts).

Now you're talking about taking the same lens and mounting it on two different cameras. That's a different comparison altogether. If it generated a sufficient image circle to cover both sensors, one could do that. To achieve the same image, you'd have to position yourself at half the distance for the larger sensor camera. And yes, you could still stop down 2 stops and bump the ISO for roughly equivalent noise performance (assuming same number of pixels and equivalent noise reduction technology). I'm not sure the DOF would turn out the same in this case.

 

[RRJackson]

That is true, but it may not be much more useful than a 70-200 f/4 on
full frame. [It could still be a better lens than any particular
70-200 f/4, of course]

I dunno. Look, lenses for smaller film formats were always faster. I used to shoot a lot of Super-8 with a Beaulieu 7008 fitted with a Schneider-Kreuznach 6-70mm f/1.4 lens. On a 35mm camera the equivalent lens would be something around a 24-280mm f/1.4 lens. The problem is that both my 35mm and Super-8 cameras were limited by Kodak Vision 500T as their fastest stock (assuming I bought cut-down 500T from Pro8mm, which I often did). So I got used to the Super-8 camera having the DOF of a camera with an f/5.6 lens, but being able to expose in much lower light.

I also have a Canon Scoopic 16M 16mm camera with a 12.5-75mm f.1.8 lens. So now the film is four times the size of Super-8 (and the grain is much less noticeable), but the lens is 2/3 of a stop slower and has roughly the range of a 25-150mm lens would have on my 35mm cameras. I'm still able to expose the film at f/1.8 and 500 ISO (cause faster film isn't really available), but now I'm working with only twice as much DOF as 35mm instead of four times as much. And this is where it gets interesting, IMO, because 35mm cinema cameras don't run the film from side to side like still cameras. They run it from top to bottom, which yields a frame almost exactly the same size as APS sensors and the DOF wide open is still shallow enough that you can't really eyeball focus. You pretty much have to use a tape-measure. So doing run-and-gun shooting it's about a thousand times easier to use 16mm. And now that the negative doesn't have to travel through duplication stages (interpositive, internegative) it's not a bad origination format. Technology has improved its usability because now you can scan it in and never suffer generation loss. Even old Ektachrome 16mm reversal stock ("Film at 11!") looks pretty good now. Here's an Ektachrome 7240 scan from some stuff I shot a couple of years back. That's a 1920x1080 frame grab right off the 1080p telecine that I had Bono Labs do in Apple ProRes422. And even with the dust and scratches that pop up I'm still happy shooting it.

http://flickr.com/photos/r_jackson/1719988435/



So here's the thing. Yeah, the faster lenses are a perk of the smaller sensor size, but they aren't "equivalent" to lenses half as fast. They're fast lenses that have field of view and DOF characteristics typical of smaller sensors. But here's the rub. Olympus builds their fast lenses to perform exceptionally well wide open. Go through test data for the pro line of lenses. You usually see a marginal improvement at f/2.8 in vignetting and corner softness and then it's pretty linear until diffraction sets in. That's Olympus' ethic about fast glass meeting up with that big ol' 4/3 lens mount being about twice the width of the sensor. That is not the case with most other manufacturers' lenses, which usually require a little stopping down before they behave properly. So the Oly glass isn't usually "just a stop" faster. In practice it's usually more like two or three stops faster, if you want to compare apples to apples.

To me this is win-win. I can shoot at f/2, get DOF comparable to f/4 on a camera with a bigger sensor (which is still plenty thin...check out the background on that 16mm image shot with an "equivalent" DOF in 35mm-speak of about f/4) and still expose the image at a lower ISO, which may or may not be significantly noisier than a competing camera at the same ISO, but so what? Is it such a burden to shoot at 800 when the other guys are shooting at 1600? Particularly since the extra DOF is going to yield more keepers?